2D aperture synthesis for Lamb wave imaging using co-arrays

2D ultrasonic arrays in Lamb wave based SHM systems can operate in the phased array (PA) or synthetic focusing (SF) mode. In the real-time PA approach, multiple electronically delayed signals excite transmitting elements to form the desired wave-front, whereas receiving elements are used to sense scattered waves. Due to that, the PA mode requires multi channeled hardware and multiple excitations at numerous azimuths to scan the inspected region of interest. To the contrary, the SF mode, assumes a single element excitation of subsequent transmitters and off-line processing of the acquired data. In the simplest implementation of the SF technique, a single multiplexed input and output channels are required, which results in significant hardware simplification. Performance of a 2D imaging array depends on many parameters, such as, its topology, number of its transducers and their spacing in terms of wavelength as well as the type of weighting function (apodization). Moreover, it is possible to use sparse arrays, which means that not all array elements are used for transmitting and/or receiving. In this paper the co-array concept is applied to facilitate the synthesis process of an array's aperture used in the multistatic synthetic focusing approach in Lamb waves-based imaging systems. In the coherent imaging, performed in the transmit/receive mode, the sum co-array is a morphological convolution of the transmit/receive sub-arrays. It can be calculated as the set of sums of the individual elements' locations in the sub-arrays used for imaging. The coarray framework will be presented here using two different array topologies, a 1D uniform linear array and a cross-shaped array that will result in a square coarray. The approach will be discussed in terms of array patterns and beam patterns of the resulting imaging systems. Both, theoretical and experimental results will be given.